Trump praises Kim Jong-un 'courage' at UN

US President Donald Trump has praised North Korea's leader Kim Jong-un for his courage in taking steps to disarm, but said much work still had to be done and sanctions must remain in place on North Korea until it denuclearises.

"The missiles and rockets are no longer flying in every direction, nuclear testing has stopped, some military facilities are already being dismantled," Trump said in his speech to the annual United Nations General Assembly.

"I would like to thank Chairman Kim for his courage and for the steps he has taken, though much work remains to be done," Trump said.

"The sanctions will stay in place until denuclearisation occurs."

Trump's remarks on North Korea were dramatically different from those in his speech last year at the UN assembly, when he threatened to "totally destroy" North Korea and mocked the North Korean leader as "Rocket Man" on a "suicide mission".

Trump held an unprecedented summit with Kim in Singapore in June which yielded a broad pledge by Kim to "work towards" denuclearisation of the Korean peninsula.

However, Kim's commitments and actions so far have fallen far short of Washington's demands for a complete inventory of North Korea's weapons programs and irreversible steps to give up a nuclear arsenal that threatens the United States.

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Trump has nevertheless heaped personal praise on Kim and expressed enthusiasm for a second summit.

On Monday, he said he expected this to be announced "pretty soon" but that the location had yet to be determined.

During a meeting with South Korean President Moon Jae-in at the United Nations on Monday, Trump said Kim has been "really very open and terrific, frankly".

"I think he wants to see something happen."

Trump singled out Japanese Prime Minster Shinzo Abe, Moon and Chinese President Xi Jinping for their support over North Korea, in spite of some questions about the commitment of the latter two leaders to maintaining tough sanctions on Pyongyang.

At a meeting last week with Moon, Kim promised to dismantle a missile site and also a nuclear complex if the United States took "corresponding action".

Moon told an event in New York on the sidelines of the UN meeting that declaring a formal end to the 1950-53 Korean War would encourage North Korea to move further with denuclearisation.